Using AI in IOL calculations

Decades after Harold Ridley’s feat, physicians are still challenged to try and achieve emmetropia.

Every year, thousands of new ophthalmologists worldwide begin their transformation into cataract surgeons. Aspects of their new role, like mastering their surgical skills, will certainly come with time.

But one aspect, namely the precise calculation of the patient’s IOL power, is another matter altogether. More than 60 years after Harold Ridley implanted the first IOL, physicians are still challenged to consistently try and achieve emmetropia, even with modern day instruments and formulas.

It is undeniable that to achieve superior results, careful surgery needs to accompany precise preoperative lens calculation and choice. Although modern IOL formulas have come far since the early days, we still have a long way to go to help all our patients achieve the refraction they desire.

In this article, we hope to explain how, over the last four years, we have sought to find the right solutions.

The answer lies in artificial intelligence.

We believe that every eye is different and deserves to be treated differently from other eyes. Because AI is malleable enough to recognize certain known and unknown “hunches and assumptions,” it can be taught to learn the specific nuances of each type of eye. With AI, we can, in steady increments, constantly evolve towards perfect IOL calculations.


There are two modern approaches to IOL calculations: the “tried and true” mathematical formulas and newer generation formulas based on artificial intelligence and the “big data” approach. Current mathematical formulas include the Hoffer Q, SRK/T, Holladay 1 and 2, Haigis, Barrett Universal II and our Ladas super formula (LSF). Since publishing our original formula three years ago, we have worked to move into a new category of artificial intelligence (AI)-based IOL formulas. Known as LSF AI, this formula has a scaffold that is comprised of the best of all approaches.

It is important to note that almost all IOL formulas have significant overlap. The Hoffer Q, SRK/T and Holladay 1 use just two biometric input variables, corneal power and axial length, to estimate the IOL power. They have a similar backbone, other than the way they determine the effective lens position. Similarities can also be demonstrated between the Barrett Universal II and the LSF using three-dimensional plots. Further, these formulas can be compared to approaches that rely on big data alone, such as the Hill-RBF.


To think “outside a box” you have to know what’s inside it. Over the years, the greats of IOL calculations, namely Barrett, Haigis, Hoffer, Holladay, Koch and more, have contributed many formulas. These formulas have provided unique nuances that make the calculations more suitable for particular eyes that may be short or long, steep or flat and deep or shallow in their anterior chambers. We studied the formulas and learned each of their subtle differences, such as how the effective lens position (ELP) was calculated for a particular eye. We also determined that to prove any of these calculations would require enormous numbers of eyes, so reviewing the outcomes independently would be impossible. We also learned that any attempts to statistically identify the subtle differences between each of these formulas and make minor changes to improve them would be nearly impossible without access to an enormous number of eyes.

We considered the thought process and intuition behind the nuances of formulas we know: Koch’s suggestion of an axial length adjustment, Holladay’s use of many variables, Hoffer’s demonstration that axial length is formula-specific and that a patient’s gender may play a role, and Haigis’ point that lens geometry mattered. We considered how the formulas and these adjustments would be affected by including other variables, such as posterior corneal power, a specific lens design or perhaps an aphakic refraction.


In 2015, Uday Devgan, MD, Albert Jun, MD, PhD, and the authors proposed a way of thinking about these formulas in three dimensions.1 Using a graphical representation allowed us to compare and contrast the existing formulas to see where they overlapped or differed. Then, we took each formula’s strengths and combined them into a single, “super surface” representative of a “super formula” (Figure 1). This allowed for further improvements with numerous variables to achieve greater accuracy in IOL power calculation.

Figure 1. The scaffold of the Ladas super formula.

At ASCRS, we will be presenting how our AI methodology can statistically improve outcomes in just 100 eyes. If the idea of doing so sounds far-fetched, then below are a few examples of formula adjustments using fewer eyes.

Most lens companies suggest that the A-constant should be adjusted based on a random sample of 20 outcomes. Ken Hoffer, MD, suggested using his formula for short eyes based on a study that included 36 eyes in that particular range.2 Sam Masket, MD, came up with a regression adjustment for both hyperopic and myopic LASIK-based on 30 eyes. Wolfgang Haigis, MD, adjusted his formula into the postrefractive Haigis-L based on about 40 eyes.3

We put artificial intelligence to the test to see if it would replicate the Wang-Koch adjustment for highly myopic eyes.4 Using many more eyes as data points, we verified that it is a true phenomenon.

Even more interesting is that we can further show that it doesn’t just miraculously start at an axial length of 25 mm, but rather the adjustment relates to other variables such as corneal power, anterior chamber depth and keratometry. Our artificial intelligence methodology is poised to further refine the calculations in all eyes, not just myopes.

These “intuitions” don’t occur in a vacuum but require the existence of a constellation of relationships that are dependent on many variables. How could one possibly incorporate all the possible adjustments, factors and intuitions? We believe that the answer lies in harnessing the power of artificial intelligence.


To use artificial intelligence to help solve our problems, we first needed to teach it. Figure 2 demonstrates a schema of how artificial intelligence is used to generate an “answer.” The user provides real data that includes the important input variables (such as AL, K, ACD) and a known outcome. The hidden “inner layers” of the AI weigh all the variables appropriately and predict an IOL power value that is consistent with a given data set at that moment in time.

Figure 2. Schema of AI-integrated IOL formula.

While this is a great approach to solving these problems, there are potential challenges to using this methodology alone. If a calculation is in a region with little data, the AI can be unreliable or “out of bounds.” Another issue is that the AI algorithm cannot evolve or adjust itself when input variables change. So, if we learned that a new variable, such as posterior corneal power, could bring us closer to perfection in IOL power calculation, we would need to “re-teach” the algorithm in order to refine the results.

Our unique AI approach is constantly evolving by using both the individual surgeon’s data and system-wide, big data from the an entire library of several surgeons.


The Ladas AI approach harnesses the power of artificial intelligence while mitigating its negative aspects. Our original formula acts as the ideal blueprint for the baseline, which eliminates the issue of “out of bounds” calculations. Then, if we want to evolve or add variables, the current formula can instantly learn any new adjustments as they relate to all new and existing variables.

Euclid, the father of geometry, proposed a mathematical concept about 2,500 years ago that stands true today. To describe an object’s displacement, he said, start from its point of origin. We can use this enduring concept by allowing the original Ladas formula to be the “origin” and AI and big data to figure out the “displacement” from perfection.

Distinct from the Hill-RBF, which predicts IOL power, we use the big-data approach to predict the difference or displacement between an existing formula and “perfection” for a given eye (Figure 3). These “adjustments” are not random and typically occur on the order of 0.2 D. Then, we take these predicted displacements or adjustments and seamlessly incorporate them back into the existing formula (Figure 3). Because the baseline is an already proven formula (the original LSF), we are looking for differences 100 times smaller in magnitude than the standard AI that is instead predicting IOL power. We call this “high-resolution AI.” No human could develop a formula that included every adjustment or every current or future intuitive thought.

Figure 3. Schema of Ladas super formula AI.

Figure 4. How appears when downloaded on iPhone and Android.


Consider these analogies to further explain our approach.

One involves AI and facial recognition. If a machine is asked to recreate the Mona Lisa, it will do a better job if you give it a portrait of a face to start with rather than nothing. The AI must only work on more minute adjustments, such as shaping the face, adjusting the size of features, contouring the nose and so on, rather than creating the face from scratch.

A computer can now beat every grandmaster in the history of chess, based on feeding the computer the rules of the game and letting it play the same game over and over. But, what if the rules changed in the middle of the game, and a new chess piece was introduced?

This would be the equivalent of introducing a new IOL calculation input variable, such as posterior cornea or a new lens design. Machines can quickly learn the influence of the new “rules,” weigh it appropriately in concert with other variables and evolve. Our approach is singular in that it can do so quickly.


Anyone can sign up at and use the formula, either on computer or through iPhone and Android apps. Many surgeons are contributing their postop data to enhance their own results and to participate in the big data library.

Groups of surgeons from one practice can input data, too, but these data, which are destined for the library, are handled differently. This particular formula only extracts what we regard as the most precise postop data to refine that formula. The library data are from surgeons worldwide and that proves useful in rare eyes. A busy cataract surgeon who only sees one eye a year with highly unusual parameters, such as keratometry of 50 diopters or axial length of 17 mm, will find many eyes like this in the library because of the vast number of surgeons participating.

For a high-volume surgeon, like Jonathan Solomon, MD, the Ladas group can create an individualized AI formula. Dr. Solomon is working on refining his own AI as well as contributing to the “library” data. Any surgeon who can commit 200 or more eyes worth of data can do the same.

“I have imported close to 600 [eyes],” says Dr. Solomon. “[LSF AI] provides another level of precision and accuracy beyond the existing formula due to all of the dimensions that can be input along with the refinement across different data points.”

His practice, located in three offices near Washington, D.C., has seen incremental improvements across all eyes – short/average/long axial lengths, and varying anterior chamber depth and K-values. “I am extremely impressed with it,” he says.

Residents and surgeons in training have their own platform to securely keep their outcome data and analyze it over time. We want them to get better as they get more experience doing surgery. We will help them analyze it with our formula as well as others. While these early data are not part of our refined library data, the residents and surgeons in training can access their work and monitor their outcomes. From these continually-improving residents will come our thought leaders of the future. OM


  1. Ladas JG, Siddiqui AA, Devgan U, Jun AS. A 3-D “Super Surface” Combining Modern Intraocular Lens Formulas to Generate a “Super Formula” and Maximize Accuracy. JAMA Ophthalmol. 2015;133:1431-1436.
  2. Hoffer, KJ. The Hoffer Q Formula: A comparison of theoretic and regression formulas. JCRS. 1993; 19:700-712.
  3. Haigis W. Intraocular lens calculation after refractive surgery for myopia: Haigis-L formula. J Cataract Refract Surg. 2008 Oct;34:1658-63. doi: 10.1016/j.jcrs.2008.06.029
  4. Koch DD, Hill W, Abulafia A, Wang L. Pursuing perfection in intraocular lens calculations: I. Logical approach for classifying IOL calculation formulas. J Cataract Refract Surg. 2017;43:717-718.

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